There is a problem with my strawberry, see the photos
It's been growing in this container for about four months. It grows indoors. I have fed it recently, after that the leaves started to turn brown.
Is the plant sick? What can be done about it?
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You are overwatering. I can see a line on the pot, in the saucer, where the water level usually is. The soil also looks very wet. That is far too much water for a strawberry plant. The leaves are also showing signs of nitrogen burn. It may be too late, but you can give it another shot.
You should immediately dump out that saucer, and repot the plant as soon as possible. Remove the plant from the pot, and clean the roots well, trying not to damage them. Cut off any rotten/dead roots. Be thorough. There may not be many healthy roots left. I usually dust very lightly with a fungicide powder/rooting hormone to keep it from spreading, and promote regrowth. Then, cut off all leaves that have the brown rot on them. Dispose of all old soil and plant cuttings far from the plant, and its new soil and pot.
Time to repot. Use a high quality unfertilized potting mix (the plant isn't in good enough shape to handle the amount of n-p-k found in fertilized mix. I'd use a different, similarly sized pot (the old one may contain disease), and plant the plant in it, making sure the roots are spread well, not cramped together at all. Plant it a little higher than it is now (it's somewhat too low). The crown should emerge from the soil, almost as much as it sinks in. Then water, enough to get the potting soil moist, but not soaked.
Keep the soil slightly damp until the plant shows signs of recovery, if it does. This will be seen as new green leaves emerging from the crown. If you see this, change your watering schedule. You want to water until it runs from the pot, and then leave it until the top 1/4-1/2" of mix has completely dried. Then repeat. Do not ever let it sit in a saucer of water. If you water, and there is a significant amount of water in the saucer, dump it out.
Only after the plant is starting to pick it up, and grow well, should you begin fertilizing again. Try giving it half strength solutions at first, every other week, until the plant is much stronger. Then you can feed as normal. It will eventually need a larger pot (that one isn't big enough for a full sized strawberry plant.
Update: I didn't notice an indoors tag on the question (added now). This explains some other symptoms. Regular strawberry plants don't make the best houseplants. They like lots of light, and most kinds want a dormant rest period over winter. Yours is showing some signs of real etiolation. The stems are long, the leaves are small and pale. It needs more light. They depend on daylight length for the most part, to determine seasons. Now, indoors, they will need to have very bright supplemental lighting in order to be healthy. This will have to be set, or manually turned on at sunrise/off at sunset for the most natural growth.
Over winter, the plant will need to rest, or go dormant. Warm temperatures will confuse the plant, and it needs cold temperatures. Over winter, it shouldn't get much over 45 degrees Fahrenheit if possible. That's the biggest reason why they (as well as many other temperate perennials) make poor houseplants.